"Three months ago today he walked me down the aisle & now he is walking with the angels," Sarah shared in her heartfelt post.
"I’m left with a hole in my heart & 34 years of beautiful memories... growing up together as children into adults.
"You fought THE BRAVEST battle Big Squirt to the very end and I promise to always live by your standards; to remember what you taught me, “it’s all about the journey, not the destination” & “have no regrets”.
Sarah's emotional tribute went on to say how much she loved her big brother, along with sharing a number of photographs of him.
"I love you, I cherish you, I salute you," she said.
"You can rest now, we know you’re dancing up there in the heavens, always watching down on us. Forever all my love, Medium Squirt."
Karl, who was originally from Melbourne, had walked the actress down the aisle at her wedding to James Stewart in July.
The ceremony was held in Ireland so that Karl, who was unable to travel due to his treatment, could attend the celebrations.
Sarah told WHO magazine in August: "My brother lives [there]. He's not able to fly at the moment because of health reasons."
Karl's death was also marked in a death notice in Ireland on Wednesday.
According to the announcement, Karl passed away peacefully at Beaumont Hospital on October 23.
He was the "beloved husband of Susana, loving father of Alexander and Aurora, and son of Sharma and Neil. Very sadly missed by his wife, children and parents, his brother Rowan, sisters Sarah and Lauren, extended family in Australia, neighbours and friends."
One of Karl's final tweets showed his determination to overcome his cancer.
"Boom! That's 2 rounds of chemo. 4 to go - Bull Island, Clontarf," he posted on September 11.